Electric Flux Calculator
Calculate electric flux through a surface using Φ = E·A·cos(θ).
Also applies Gauss's law to find the enclosed charge from flux.
Electric flux measures how much electric field passes through a surface:
Φ = E × A × cos(θ)
And Gauss’s law relates flux to enclosed charge:
Φ = Q_enclosed / ε₀
Where:
- Φ = Electric flux (N·m²/C or V·m)
- E = Electric field strength (N/C = V/m)
- A = Area of the surface (m²)
- θ = Angle between the electric field vector and the surface normal
- Q_enclosed = Total charge enclosed by the Gaussian surface (C)
- ε₀ = Permittivity of free space = 8.854 × 10⁻¹² C²/(N·m²)
Understanding the angle θ:
- θ = 0°: Field is perpendicular to the surface (maximum flux)
- θ = 90°: Field is parallel to the surface (zero flux — field “slides along” the surface)
- θ = 180°: Field is anti-parallel to surface normal (negative flux)
Gauss’s Law application: The total electric flux through any closed surface equals the enclosed charge divided by ε₀. This makes calculating electric fields from symmetric charge distributions very easy:
- Sphere of charge: flux = Q/ε₀ regardless of sphere size
- Infinite plane of charge: flux through box = σA/ε₀
Physical intuition: Think of electric flux like counting how many electric field lines pass through a surface. More field lines = stronger field or larger area = more flux.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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